MANNER or PRODUCTION OF MUTATIONS 501 



tion-by-breakage interpretation of the linearity of lethal frequency at 

 high doses. For one thing, it is known from direct tests of the matter 

 that lethals constitute but a relatively small minority of gene mutations 

 (see Chap. 7). There is no good ground for regarding them as being 

 produced by a different mechanism from the others, and no sharp line 

 between lethal and other gene mutations exists. Yet if all or most 

 changes classified as gene mutations were produced in connection with 

 breaks, only a small minority of breaks could be connected with lethals 

 (or steriles). Thus the high frequency of occurrence of lethal (and 

 sterile) effects in connection with structural changes would still require 

 the position-effect explanation. 



Second, the mutation-by-breakage interpretation by itself would lead, 

 not to a linear relation^ between lethal frequency and dose at high doses, 

 but to an ever more marked drop in the frequency below linearity as the 

 dose was increased. The major reason for this is that half the gross 

 structural changes involving two breaks and a still higher proportion of 

 those involving more than two breaks are of aneucentric type and there- 

 fore go unrecorded. Hence if the primary breaks were associated with 

 lethals, a part of these lethals would be lost from the record. As the 

 dose rose this loss would become greater, relatively to the total number 

 of breaks (and therefore of lethals), both because the structural changes, 

 unlike the breaks themselves, increase as a power of the dose higher than 1 

 and because the more complicated structural changes, formed with rela- 

 tively higher frequency than the others at higher doses, are especially 

 likely to be aneucentric. In addition to these losses of lethals which 

 might have been associated with primary breakage, there would similarly 

 be losses of those lethals involving two breaks close together, which would 

 have appeared as small deletions had they not become involved in aneu- 

 centric gross structural changes. Results on translocations involving 

 rings (Muller, Makki, and Sidky, 1939; Muller, 1940) showed, in fact, 

 that there is an unusually high chance of intrachromosomal rearrange- 

 ments becoming drawn into more complicated combinations. The result- 

 ant over-all reduction in lethal frequency below linearity at high doses, 

 due to all these causes, as calculated on the assumption of most breaks 



^ It is, of course, assumed, when a linear relation is referred to, that allowance has 

 been made for the so-called "saturation effect," that is, for the cases of simultaneous 

 occurrence of two or more independently arisen lethals (see Muller, 1936b). If, as 

 is usually the procedure, such cases are counted as one lethal, the frequency of recorded 

 lethals in a situation in which the actual lethal frequency was proportional to dose 

 would follow the formula 1 — (1 — ly, where I is the frequency per unit of dose and 

 d is the dose. (This may also be expressed as 1 — e-"'^, where e is the base of natural 

 logarithms and —a is the natural logarithm of 1 — /.) The resulting line is at first a 

 straight one, but its slope gradually diminishes at higher doses. The statement that 

 the frequency falls below that expected on linearity therefore implies that it falls 

 more rapidly than the saturation effect alone would allow. 



